Chapter 30 Review: Lenses

• Glass of a certain shape can form an image that appears larger, smaller, closer, or farther than the object being viewed.
• Today eyeglasses allow millions of people to read in comfort, and cameras, projectors, telescopes, and microscopes widen our view of the world.

Important Terms You Should Know:
aberration
astigmatism
converging lens
cornea
diverging lens
eyepiece
farsighted
focal length
focal plane
focal point
iris
lens
nearsighted
objective lens
principal axis
pupil
ray diagram
real image
retina
virtual image

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30.1 Converging and Diverging Lenses

• When a piece of glass has just the right shape (or other transparent material), it bends parallel rays of light so that they cross, or appear to cross, and form an image at a single point. This is called a lens.
• lenses manipulate light; they may be thought of as a set of prisms that when arranged in certain positions, the prisms bend incoming parallel rays so they converge to (or diverge from) a single point.
• Here is an example of the two types of lenses: converging and diverging.
  • a converging lens is thicker in the middle, meaning that the initially parallel rays of light passing through are made to converge (or to meet at a point). in this type of lens, the wave fronts are retarded more through the center of the lens, which allows the light to converge.
  • a diverging lens is thinner in the middle and allows for parallel rays of light to be diverged (or to extend from different directions from a point). In this type of lens, the waves are retarded more at the edges.
    
    
    

    Diagram of converging and diverging lenses.

    
    
    http://www.math.ubc.ca/%7Ecass/courses/m309-01a/chu/MirrorsLenses/converge-diverge.gif
    
    
    

    Shape formation of converging and diverging lenses, or concave and convex lenses.

    
    

http://www.glenbrook.k12.il.us/gbssci/phys/CLass/refrn/u14l5a2.gif

• the most net bending of rays occurs at the outermost prisms, for they have the greatest angle between the two refracting surfaces. not net bending happens in the middle prism because its glass faces are parallel and rays emerge in their original direction.
• real lenses are not made of prisms but of a solid glass piece with surfaces that are normally ground down to spherical shape.

• here are some crucial terms that make up a lens:
  • principle axis: this is the line joining the centers of curvature of the surface of the lens.
  • focal point: for a converging lens, the point at which a beam of light parallel to the principal axis converges. for a diverging lens,the point from which such a beam appears to come. incident parallel beams that aree not parallel to the principal axis focus at ponts above or below the focal point.
  • focal plane: a plane passing through either focal point of a lens that is perpendicular to the principal axis. For a converging lens, any incident parallel beam of light converges to a point somewhere on a focal plane. For a diverging lens, such a beam appears to come from a point on a focal plane.
    • a lens has two focal points and two focal planes because a lens affects light coming from the right the same way as light coming from the left.
  • focal length: whether converging or diverging, the focal length is the distance between the center of the lens and its focal point. when the lens is thin, the focal lengths on either side are equal, even when the curvatures on the two sides are not.

30. 2 Image Formation by a Lens

• with unaided vision, a far away object is seen through a small angle of view but when you are closer, the same object is seen through a larger angle of view. This wider angle enables the perception of more detail. Magnification happens when an image is observed through a wider angle with the use of a lens than without the lens and allows more detail to be seen.
• a magnifying glass is a converging lens that increases the angle of view and allows more detail to be seen. A converging lens will only magnify when the object is between the focal point and the lens, which is why you have to hold the magnifying glass up close to the object you are observing.
  • the magnified image will be farther from the lens and will appear right-side up. If a screen were set at the image distance, no image would appear on the screen because no light is actually directed to the image position. However, the rays that reach the eye behave as if they came from the image position, making this image a virtual image. A virtual image is formed through reflection or refraction that can be sen by an observer but cannot be projected on a screen because light from the object does not actually come to a focus.

Ray diagram for a diverging lens that forms a virtual image

http://www.lhup.edu/%7Edsimanek/scenario/labman3/thinlens.htm

• when the object is far enough away to be beyond the focal point of a converging lens, light from the object does converge and can be focused on a screen, making this image a real image. A real image formed by a single converging lens is upside down or inverted.

Ray diagram for a converging lens that forms a real image.

http://www.lhup.edu/%7Edsimanek/scenario/labman3/thinlens.htm

• converging lenses are used in projecting slides and motion pictures on a screen and for projecting a real image on the film of a camera.
• when a diverging lens is used by itself, the image result is always virtual, right-side up, and smaller than the object itself.
  

  A virtual image produced by a converging lens

  
  http://www.lostartofblogging.com/wp-content/uploads/2007/12/magnifying-glass.JPG
  • a simple use for a diverging lens would be for the viewfinder of a camera. When you look through the viewfinder at the object you want to take a picture of, you see a right-side up, virtual image that matches the same proportions as the photograph to be taken.

30. 3 Constructing Images Through Ray Diagrams

• ray diagrams show the principal rays that can be used to determine the size and location of an image.
  • in order to construct a ray diagram three things must be known:
    1. the size and location of the object
    2. the objects distance from the center of the lens
    3. the focal length of the lens
  • to locate the position of the image,you only have to know the paths of two rays from a point on the object.

Different types of rays in a ray diagram

http://facstaff.gpc.edu/~pgore/PhysicalScience/optics.html

• a ray parallel to the principal axis will be refracted by the lens to the focal point.
• a ray of light will pass through the center with no appreciable change in direction. a ray from the tip of the arrow proceeds in a straight line through the center of the lens.
• a ray of light that passes through the focal point in front of the lens emerges from the lens and proceeds parallel to the principal axis.

these three paths are shown in the above figure: the image is located where the rays intersect. any two of these rays is sufficient to locate the relative size and location of the image.

• in the case where the distance from the lens to the object is less than the focal length, the rays diverge as they leave the lens. the rays of light appear to be coming from a point in front of the lens. the location of the image is found by extending the rays backwards to where they meet.

Ray diagram for a magnifying glass

http://www.antonine-education.co.uk/physics_a2/options/Module_6/Topic_2/Ray_Diag_B1.gif

• the following ray diagrams show image formation by a converging lens as an object initially at the focal point in moved away from the lens along the principal axis. Since the object is not located between the focal point and the lens, all the images that are formed are real and inverted:

1.)

Ray diagram for an object between f and 2f from lens

http://www.antonine-education.co.uk/physics_a2/options/Module_6/Topic_2/Ray_Diag_A3.gif

Object Position: between f and 2f from lens
Image Position: beyond 2f from lens
Image size: magnified

2.)

Ray diagram for an object that has a distance f from lens (at focal point)

http://www.antonine-education.co.uk/physics_a2/options/Module_6/Topic_2/Ray_Diag_A4.gif

Object Position: distance f from lens (at focal point)
Image Position: infinity

3.)

Ray diagram for an object that has a distance 2f from lens

http://www.antonine-education.co.uk/physics_a2/options/Module_6/Topic_2/Ray_Diag_A2.gif

Object Position: distance 2f from lens
Image Position: distance 2f from lens
Image Size: same as object

4.)

Ray diagram for an object that is beyond 2f from lens

http://www.antonine-education.co.uk/physics_a2/options/Module_6/Topic_2/Ray_Diag_A1.gif

Object Position: beyond 2f from lens
Image Position: between f and 2f from lens
Image size: smaller

• drawing ray diagrams also works for diverging lenses. a ray parallel to the principal axis from the tip of the arrow will be bent by the lens in the same direction as if it had come from the focal point. A ray through the center goes straight through. A ray that is heading for the focal point on the far side of the lens is bent so that it emerges parallel to the axis of the lens.

Ray diagram for a diverging lens

http://www.physics.uq.edu.au/courses/phys1000/optics_raydiag2.png

• the three rays appear to come from a point on the same side of the lens as the object
• this point defines the position of the virtual image
• the image is nearer the lens than the object
• it is smaller than the object and right-side up
• to get a better understanding of how real and virtual images are formed, visit this web page to take a look at ray diagrams for the case of converging and diverging lenses:
  • http://hbar.phys.unca.edu/bennett_phys222/Content/labs/ray/ray_principles.asp

30.4 Image Formation Summarized

• Converging lens: a simple magnifying glass when the object is within one focal length of the lens
  • image is virtual, magnified, and right-side up.
    • when the object is beyond one focal length = real, inverted image
    • the location of the image depends on how close the object is to the focal point. If it is close to the focal point the image is far away ( movie or slide projector)
    • if the object is far from the focal point, the image is nearer ( as with a camera)
    • in all cases where a real image is formed, the object and the image are on the opposite sides of the lens.
• Diverging Lens:
  • the image is always virtual, reduced, and right-side up.
  • this is true for all locations of object
  • in all cases when i virtual image is formed, the object and the image are on the same side of the lens

30.5 Some Common Optical Instruments

• camera
• telescope
• compound microscope
• projector

The Camera:

http://www.kenrockwell.com/nikon/d40/images/D3S_2078-600.jpg

Diagram showing how light enters a camera, similar to that of the eye

http://www.pasadenaeye.com/faq/faq15/faq15_text.html


consists of a lens and a sensitive film mounted in a lightweight box. the lens is mounted so that it can be moved back and forth to adjust the distance between the lens and film. the lens forms a real, inverted image on the film.

• most cameras use compound lenses to minimize distortions produced by a lens called aberrations.
• the amount of light allowed to pass through is regulated by a shutter and diaphragm.
• the shutter controls the length of time that the film is exposed to light
• the diaphragm controls the opening that light passes through to reach the film

The Telescope:

Diagram A shows a ray diagram for an astronomical telescope

http://www.lhup.edu/~dsimanek/scenario/telescop.gif

paying attention to the diagram A, it shows a lens arrangement for an astronomical telescope.

• a simple telescope uses a lens to form a real image of a distant object
• it is projected in space to be examined by another lens used as a magnifying glass
• the second lens, called the eyepiece, is positioned so that the image produced by the first lens is within one focal length of the eyepiece.
• the eyepiece forms a larger, virtual image of the real image.
• when looking through a telescope, an image of an image is seen.
• astronomical telescopes produce inverted images, which is why maps of the moon are uspide down.
• a third lens (or reflecting prisms) is used in terrestrial telescopes, which make an image that is right side up
  • this type of lens is used in binoculars, having a pair of prisms side by side each with a pair of prisms to provide four reflecting surfaces to turn images right side up.
• telescopes that use lenses are refracting telescopes.

The Compound Microscope:

Ray diagram showing how the compound microscope works

http://img.tfd.com/mgh/cep/thumb/Compound-microscope-diagram.jpg

• uses two converging lenses of short focal length
  • the first lens is called the objective lens and produces a real image of a close object.
  • the image is enlarged because it is farther from the lens than the object
  • the second lens, the eyepiece, forms a virtual image of the first image, and is enlarged even more.
• this instrument is called a compound microscope because it enlarges an already enlarged image.

The Projector:

• a concave mirror reflects light from an intense source back onto a pair of condenser lenses.
• the condenser lenses direct the light through the slide or movie frame to a projection lens.
• the projection lens is mounted in a sliding tube so that it can be positioned back and forth to focus a sharp image on the screen.

30.6 The Eye:

The human eye and its components, showing how light enters through the cornea and where it converges

http://wpcontent.answers.com/wikipedia/commons/thumb/1/1e/Schematic_diagram_of_the_human_eye_en.svg/325px-Schematic_diagram_of_the_human_eye_en.svg.png

example of the human eye and how light is transferred through it

http://www.pasadenaeye.com/faq/faq15/faq15_text.html

• the human eye is similar to a camera
• the iris, or colored part of the eye, regulates the amount of light that is permitted to enter the eye through the pupil, or opening through which the light actually passes.
• the transparent covering over top of the eye is called the cornea.
• once the light passes through the cornea, is regulated by the iris, and goes through the pupil, it is focused on a layer of tissue at the back of the eye called the retina, which is extremely light sensitive.
  • the retina is not uniform
  • there is a spot in the retina where the nerves carrying all the information leave the eye in the bundle which is called the blind spot.
• the fovea is the small region in the center of the field of view where there is the most distinct vision; this is where much more detail can be viewed than at the sides of the eye
• in both the camera and the eye the image is upside down and is able to be altered for both:
  • in a camera you can turn the film around to observe it
  • in the eye, your brain has learned to turn around the images it receives from the retina
• in the eye, most of the focusing is done by the cornea
  • adjustments in focusing of the image on the retina are made by changing the thickness and shape of the lens to regulate its focal length which is called accommodation and happens courtesy of the ciliary muscle which surrounds the lens.

30.7 Some Defects in Vision

• the eyes of a farsighted person form images behind the retina because the eyeball is too short
• farsighted people have to hold objects more than 25 cm away to be able to focus on them
• the remedy is to increase the converging effect on the eye by wearing eyeglasses or contact lenses with converging lenses
• this will converge the rays that enter the eye sufficiently to focus them on the retina instead of behind the retina.
• farsightedness and nearsightedness:

Nearsightedness shown at the top: when light converges before the retina. Farsightedness: when light converges beyond the retina

http://www.hipusa.com/webmd/images/health_and_medical_reference/eye_health/understanding-vision_problems-basics-myopia-and-hyperopia.jpg

• nearsighted people can see nearby objects clearly, but does not see distant objects clearly because they are focused too near the lens, in front of the retina because the eyeball is too long
• Astigmatism is ad effect of the eye that is a result of the cornea being curved more in one direction than the other
• the eye then cannot form sharp images
• wearing corrective cylindrical lenses that have more curvature in one direction would be a solution to this defect

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30. 8 Some Defects of Lenses

• Aberrations are the distortions of an image, because no lenses produces a perfect picture
• in order to eliminate this problem some lenses can be combined in certain positions to fix it, most optical instruments use compound lenses that consist of several simple lenses
• Spherical aberration happens when light passes through the edges of a lens and focuses at a different place from light passing through the center of the lens
• this can be revised by covering the edges of a lens
• in optical instruments, it is revised by a combination of lenses

The above image is an example of spherical abberation. The image below is an example of chromatic abberation

http://upload.wikimedia.org/wikipedia/commons/thumb/9/92/Spherical_aberration_2.svg/371px-Spherical_aberration_2.svg.png

• Chromatic aberration is a result of the different speeds of light of various colors and the different refractions that take affect on them
• through out a simple lens blue and red light bend by different amounts so they do not focus in the same spot
• Achromatic lenses correct this defect due to the combination of simple lenses of different types of glass
• vision is sharpest in the eye when the pupil is the smallest it can be
• this is so because light then passes through only the center of the eye's lens in which spherical and chromatic aberrations are limited
• light bends the least through the center of the lens so less focusing is required for a sharp image
• vision is better in bright light as opposed to darkness because your pupils are smaller
• in today's world, eyeglasses and contact lenses are becoming more and more of a thing of the past
• surgeons are able to reshape the cornea of the eye which allows for normal vision, via experimental techniques

Works Cited:

All information gathered was courtesy of the text book and outside sources:
Hewitt, Paul G. Conceptual Physics. Third Edition ed. Menlo Park, California: Scott Foresman Addison Wesley, 1999.

How Does the Human Eye Work? 1998-2003. Pasadena Eye Associates. 28 May 2009 <http://www.pasadenaeye.com/faq/faq15/faq15_text.html>.

Lens (optics). Wikipedia. May 2009 <http://en.wikipedia.org/wiki/Lens_(optics)>.

http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/lenscon.html